Biomedical Engineering Reference
In-Depth Information
Table 6.1
List.of.No
tations
Notation
Meaning
N
A.set.of.grids.{1,.2,.3,.…,|
N
|}
T
A.set.of.terminals.{1,.2,.3,.…,|T|}
T
|}
d
ij
The.distance.connection.cost.between.WLL.terminal.
i
and.the.repeater.installed.
on.grid.
j
.∀
i
∈
T
,.∀
j
∈
N
C
r
The.installation.cost.of.the.repeater.on.each.grid
The.cost.coefficient.of.the.repeater.antenna.with.respect.to.its.gain
α
(
G
r
)
j
The.antenna.gain.of.the.repeater.using.on.grid.
j
.∀
j
∈
N
C
max
The.maximum.capacity.of.each.repeater
P
0
The.transmission.power.of.the.WLL.base.station
G
b
The.antenna.gain.of.the.WLL.base.station
L
j
The.total.path.loss.on.grid.
j
.∀
j
∈
N
P
r
The.required.minimum.received.signal.strength.at.the.WLL.repeater
R
min
The.minimum.allowed.total.number.of.repeaters.to.be.installed
R
max
The.maximum.allowed.total.number.of.repeaters.to.be.installed
x
ij
Equal.to.1.if.WLL.terminal
i
is.connected.to.the.repeater.installed.on.grid.
j
and.0.
otherwise.∀
i
∈
T
,.∀
j
∈
N
y
j
Equal.to.1.if.a.repeater.is.installed.on.grid.
j
.and.0.otherwise.∀
j
∈
N
z
j
Equal.to.1.if.a.terminal.is.located.on.grid
j
and.0.otherwise.∀
j
∈
N
Source:
Data.from.Chan,.T..M.,.Man,.K..F.,.Tang,.K..S.,.Kwong,.S.,.Multiobjective.optimization.
of.radio-to-iber.repeater.placement.using.a.jumping.gene.algorithm,.in.
Proceedingsof
IEEE International Conference on Industrial Technology
,. Hong. Kong,. China,. December.
2005,.291-296.)
6.3 MathematicalFormulation
In.this.repeater.placement.problem,.the.objective.was.to.minimize.the.total.
repeater.cost.and.total.link.cost.simultaneously..The.mathematical.model.
in.Park,.Song,.and.Bae.[17].was.adopted,.and.the.notations.used.are.given.
The. objective. functions. were. specified. by. two. types. of. costs:. the. total.
repeater.cost,.including.the.cost.of.repeater.installation.and.repeater.anten-
nas,.and.the.total.link.cost.between.WLL.terminals.and.repeaters,.which.was.
calculated.as.the.Euclidean.distance.between.a.WLL.terminal.and.a.repeater..
In.mathematics,.minimize.the.following.two.functions:
∑
(
)
(
)
Total.repeater.cost:.
f
=
C
+ α ⋅
G
⋅
y
.
(6.5)
1
r
r
j
j
j N
∈
.
∑
Total.link.cost:.
f
=
d x
ij
.
(6.6)
2
ij
.
i T
∈
j N
∈
Search WWH ::
Custom Search